November 27, 2009
A low-noise, high-dynamic-range, digital receiver for radio
astronomy applications: An efficient solution for observing
radio-bursts from Jupiter, the Sun, pulsars, and other astrophysical
plasmas below 30 MHz
V.B. Ryabov
1, D.M. Vavriv
2, P. Zarka
3, B.P. Ryabov
2, R. Kozhin
2, V.V. Vinogradov
2, and L. Denis
41 Future University-Hakodate, 116-2 Kamedanakano-cho, Hakodate, Japan 041-8655 e-mail: [email protected]
2 Institute of Radio Astronomy, 4 Krasnoznamennaya St, 610002 Kharkov, Ukraine
3 LESIA, Observatoire de Paris, CNRS, UPMC, Universit´e Paris Diderot, 5 Place Jules Janssen, 92190 Meudon, France 4 Station de Radioastronomie, USN, Paris Observatory, 18330 Nanc¸ay, France
Received ; accepted
ABSTRACT
A new two-channel digital receiver that can be used for observing both stationary and sporadic radio sources in the decameter wave band is presented. Current implementation of the device operating at the sampling frequency of 66 MHz is described in detail, including the regimes of waveform capture, spectrogram analysis, and coherence analysis (cross covariance between the two inputs). Various issues pertaining to observational methods in the decameter waveband affected significantly by man-made interferences have been taken into account in the receiver design, as well as in the architecture of the interactive software that controls the receiver parameters in real time.. Two examples of using the receiver with the UTR-2 array (Ukraine) are reported: S-bursts from Jupiter and low-frequency wide-band single pulses from the pulsar PSR0809+74
Key words.Instrumentation: miscellaneous – Methods: observational – Planets and satellites: individual: Jupiter – pulsars: general – pulsars: individual: PSR0809+74
1. Introduction
The Low Frequency (LF) band of radio waves is the least stud-ied range in radio astronomy because of the numerous technical difficulties caused by the properties of the terrestrial ionosphere (low-frequency cut-off, non-stationarity) as well as the presence of strong man-made interference signals (Weber & Faye 1998; Weber et al. 2005; Johnson et al. 2005). The interest in the fre-quency range from 10 to 100 MHz has been re-established in both the European Union and United States, where the develop-ment and construction of new large radio telescopes has initi-ated. Two large international projects can be mentioned in this respect: LOFAR (Low Frequency Array), under construction in the Netherlands; and LWA (Long Wavelength Array), which is located in the state of New Mexico. These ambitious projects also require the development of a new generation of digital spectral imagers that should help significantly to enhance our knowledge of the LF radio sky. In addition to the standard high-resolution real-time spectral analysis, these instruments will also be equipped with the tools for performing polarization measure-ments, as well as radio frequency interference (RFI) mitigation capabilities.
It should be noted, however, that the primary operating bands of both telescopes are limited to frequencies typically above 30 MHz, i.e., the very high frequency (VHF) range according to radio regulations of the International Telecommunication Union (ITU)1. This is for the same reasons that has left the whole LF
1 http://en.wikipedia.org/wiki/ITU Radio Bands
band practically unexplored until now, i.e., severe signal degra-dation caused by ionospheric propagation effects below 30 MHz ( 3-5 times the peak ionospheric plasma frequency) and to the very polluted electromagnetic spectrum below 30 MHz, where numerous short wave broadcasting stations, as well as various close-distance communication devices such as, e.g., personal communicators and Internet modems operate.
Nevertheless, the range below 30 MHz (HF range accord-ing to ITU) is of particular interest to planetary studies within the Solar system, searches for planets around distant stars (ex-oplanets) corresponding to moderate (exo-)planetary magnetic fields similar to Jupiter’s, pulsar studies allowing detailed anal-ysis of propagation effects magnified at these low frequen-cies, solar physics, and recombination lines, among other topics (Braude et al. 1978; Boishot et al. 1980; Lecacheux et al. 2004). Thus, it is important and timely to develop modern instru-mentation at non-imaging radio telescopes dedicated to the HF band, where emphasis can be placed on very high time and frequency resolution spectral analysis, waveform correla-tion analyses, multi-beam (ON/OFF) observacorrela-tions to help cor-recting for the effects of the ionosphere, and development of in-depth RFI mitigation methods with the final goal of weak source detection and analysis. Such a system is described in this paper. In 2005-2008, the receiver was tested for a fre-quency bandwidth of 33 MHz at the world’s largest de-cameter radio telescope UTR-2 (Ukraine) (Braude et al. 1978; Ryabov et al. 2004a; Lecacheux et al. 2004). A series of ob-servations were performed that targeted strong as well as comparatively weak (or even yet undetected) sources of
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radio emission known to exist in the decameter wave-band, such as Jupiter (Ryabov et al. 2007; Hess et al. 2009), Saturn (Griessmeier et al. 2008), exoplanets (Zarka et al. 2001; Ryabov et al. 2004b; Weber et al. 2007), radio pulsars, and the Sun (Briand et al. 2008; Melnik et al. 2008).
2. Receiver technical requirements and specifications
The receiver described here is a fully digital baseband device that to a large extent satisfies the modern requirements of these systems. Depending on the sampling clock frequency, it can per-form a Fourier analysis in a continuous frequency band of up to 65 MHz in two independent data streams (two input channels). The device is also capable of recording the signal waveforms, i.e., catching the output of the ADC, as well as performing real-time correlation (coherence) analysis between the two inputs. The principal technical characteristics of the receiver are listed in Table 1.
As noted above, one of the major negative impacts on re-ceiver operation is that produced by ground-based sources of ra-dio emissions and/or low earth orbit (LEO) satellites producing powerful RFI. Those signals acting at the receiver input lead to various non-linear effects that can spill the interference over the whole operational bandwidth. Such effects include, for exam-ple, saturation and clipping in the low-resolution input analog-to-digital converters, or signal distortions caused by limited dy-namic range of analog backend spectrometers, e.g., acousto-optical spectrum analyzers. The application of an automatic gain control does not typically solve the problem, since the introduc-tion of attenuaintroduc-tion results in decreasing receiver sensitivity and hence loss of the weak signals from astronomical sources within the background of strong interference. A straightforward way of overcoming this difficulty was implemented in the described device, which consists in building a baseband receiver with a high linear dynamic range using high-resolution analog to digi-tal conversion (ADC). Efficient interference suppression can be performed at later stages by applying RFI mitigation techniques (usually in the spectral domain), i.e., at the post-processing stage (Zarka et al. 1997; Rosolen et al. 1999; Weber et al. 2005; Ryabov et al. 2004b). The design of the receiver/spectrometer described in this paper has thus focused on achieving the high-est dynamic range and sensitivity, sufficient for recording weak radio sources notwithstanding strong in-band interference. The reported spurious free dynamic range (SFDR) reaches a value of about 112 dBc (decibels relative to the carrier), whereas the noise floor constitutes about -117 dBFS (decibels relative to full scale) under typical observational conditions.
Other key requirements that have also been implemented in the receiver are the flexibility of both its operation and its user interface. This becomes an important issue when taking into ac-count the sporadic character of many sources of radio emission in the decameter waveband such as, e.g., the Sun and Jupiter (Lecacheux et al. 2004; Ryabov et al. 2007), as well as the non-stationary character of multiple in-band RFI signals. The highly variable RFI environment and unpredictable signal appearance mean that active participation of the observer/operator in the data acquisition process is required or complex adaptive real-time software is needed. The problem has been addressed by the development of specialised software operating on the acquisition PC, that allows an efficient control of observational parameters. The control is achieved by means of real-time visual analysis of the output dynamic spectra or coherence function, thus enabling the observer to optimize the signal-to-noise ratio (SNR). The
software implementation includes a ramified system of menus, automatic file archiving system, and interactive real-time color-and contrast-tuning options that facilitate the process of identi-fying weak signals in noisy spectrograms, when the noise power is several orders of magnitude higher than that of the useful sig-nal. Receiver performance and adopted technical solutions are described in Appendix A.
3. Theoretical background and operation
The digital receiver can operate in three qualitatively different regimes hereafter called waveform, full power, and correlation mode. The modes are mutually exclusive, i.e., once one of them is chosen by the operator, the information that could be obtained by using other regimes is lost. This means, for example, that spectral information is unavailable in real time in the waveform mode (see below) and vice versa. In this chapter, we provide a brief description of all the operation regimes in general terms of correlation/spectral analysis.
3.1. Waveform mode
In this regime, the data streams from one or both ADC-s are di-rectly recorded to the hard disk of the host PC, without any trans-formation and/or analysis. This is, therefore, the simplest signal recording method, which shifts all the processing to subsequent stages of analysis decided by the user. This regime provides po-tentially the highest flexibility, because the post-processing steps can be developed on a trial and error basis allowing the careful selection of the data analysis method and fine tuning of every stage of calculation. The apparent drawbacks of this approach are
1. the enormous volume of data that it generates (264 MBytes/sec at 66 MHz sampling);
2. the absence of real-time spectral information on the display during data acquisition;
3. massive calculations required in the post-processing to de-termine spectral or correlation information.
The limitations of the waveform mode thus define the situa-tions where its usage is preferable. Those include the obser-vations of the sources that have high occurrence probability for the signal, i.e., are predictable, are of high SNR, and pro-duce frequency patterns in spectrograms with various time-frequency scales that require analysis at several values of res-olution. A good example of these “predictable” powerful sig-nals is decameter S-burst (“S” = short) emission from Jupiter known to have complex morphology in the time-frequency plane and high occurrence probability under certain conditions de-fined by the geometric configuration between Earth, Jupiter, and its satellite Io (Ryabov et al. 2007; Hess et al. 2009). As shown below, the waveform mode can also be used for highly dis-persed pulsar observations, since it permits spectral analysis of very fine frequency resolution and/or coherent dedispersion (Lorimer & Kramer 2005).
3.2. Full power mode
One of the standard approaches to the analysis of non-stationary sporadic signals is by means of windowed Fourier transform (Bendat & Piersol 1986) that converts a scalar input signal x(τ) into a two-dimensional spectrogram A(t, f ) (otherwise called a
Table 1. Characteristics of the digital receiver
Input-output channels 2
ADC resolution, bits 16
ADC sampling frequency, MHz
(external/internal) 10 ... 130
Input bandwidth, MHz 1 ... 65
Input impedance, Ω 50
Input signal amplitude (max), V 1
SNR, dBFS 74
SFDR, dBc >112
Noise floor, dBFS -117
Effective number of bits (ENOB) 12 FFT window length / resolution bits 16384 / 30
Time window shape User-defined
(default = Hanning) Max. number of output frequency channels 8192
(i.e., 32 MHz total band with 4 kHz resolution)
FFT window overlap 0%, 50%
Integration time 0.25 ... 128 msec
(time steps,Na) (2 ... 1024)
Accumulated values precision, bits 54
Output precision, bits 30
Complex FFT calculation time, µs 114 - Waveform
Output modes - Power spectrum
- Coherence (Cross-correlation spectrum) Digital frequency down conversion Optional
dynamic spectrum or periodogram). The function A(t, f ) is in-troduced as an average of the spectral power density of the win-dowed signal A(t, f ) = |X(t, f )|2, (1) X(t, f ) = 1 T t+T /2 Z t−T/2 x(τ) g(τ − t) e−i2π f τdτ, (2)
where g(t − τ) is the “window function” used to split the non-stationary data into approximately non-stationary segments. If a “ta-pering” shape of the window function is chosen, it also allows efficient suppression of spurious patterns in the spectrograms caused by the spilling of powerful narrow-band (broadcasting) signals and pulsed RFI emission through the side lobes of the (otherwise chosen) rectangular window. The parameter T de-fines the length of the analysis window sliding along the time axis, whereas parameter t corresponds to the position of its cen-ter in time.
The receiver performs the calculations defined by the Eqs. (1, 2) as follows. The input signal is digitized at the sampling clock rate fs of the ADC (sampling time, ∆ts = 1/ fs ). The key parameter of the DSP board used for calculating the spec-tra is the length Nw of the data segment (window) that is pro-cessed in every elementary step of computing a spectrogram. Since fast Fourier transform (FFT) is used in spectral estima-tion, the window size Nw is usually selected to be the integer power of two, i.e., Nw = 2m. This parameter defines the dura-tion of the time window T = Nw∆ts. The window size deter-mines the distance between two adjacent FFT frequency chan-nels in the spectrogram by means of the formula ∆ f = fs
Nw and thus provides a value of the highest possible frequency reso-lution that can be roughly estimated, e.g., at the 3 dB level of noise equivalent bandwidth of a frequency channel as δ f ∼ 2∆ f .
When taking into account the time-frequency duality principle (Bendat & Piersol 1986), the time resolution is also found to be dependent on the choice of window size, because it is limited at the level of ∆t ≥ ∆ f1 . This principle implies that an approximate
relation ∆t × ∆ f 1 always holds, establishing a limit for one of the resolution parameters after another has been chosen.
The resulting spectrogram is a two-dimensional array of the spectral power values, A(tk,fj), sampled on the time-frequency grid defined by the values of time and frequency resolution, i.e.,
tk = t0 + k∆t, fj = j∆ f , j = 0, 1, 2, ...,N2w − 1 . In principle, higher resolution can be achieved by reducing the values of ∆ f and ∆t, but this enhancement has certain limitations imposed by the above-mentioned time-frequency duality property.
Two other important points should also be considered. First, if a smoothing window function g(τ − t) is selected for the anal-ysis, data gaps appear at the edges of the window resulting in reduced signal power and deterioration of the signal-to-noise ra-tio. Second, the spectrogram values obtained directly using Eq. 2 are statistically inconsistent, in the sense that the variance in the spectral power does not vanish when the length of the window tends to infinity (Fitzgerald et al. 2000).
The commonly accepted practice for solving the above prob-lems consists in using overlapping data windows and averag-ing data in several consecutive segments. A larger overlap be-tween successive windows increases the averaging effect and decreases the data losses at the edges, but also increases the computational resources necessary to accomplish the calcula-tion. A compromise can be accepted at the typical level of ∼ 50% overlap that brings only about 1% reduction in the SNR (Kleewein et al. 1997). This averaging procedure was initially proposed by Tukey (1967) and has now become a traditional method (Fitzgerald et al. 2000) of enhancing the spectrograms. In short, it allows an efficient “smoothing” of otherwise noisy spectrograms at the cost of decreasing the time resolution. The
procedure of time averaging of Naadjacent spectra thus requires introduction of an additional parameter ∆tadefining the time res-olution in the smoothed spectrogram, ∆ta= Na∆t.
3.3. Correlation mode
In full power mode, the two input signals are processed in-dependently, thus producing two independent output streams. In contrast, the two input signals in correlation mode are con-verted into a single output, the value of coherence between the two input signals. The time and frequency dependent coher-ence can be used under various circumstances, when correla-tion properties between the two input signals are of interest, e.g., for suppressing confusion signals in multi-beam observa-tions (Zarka et al. 1997).
The coherence function C(t, f ) is introduced in the time-frequency plane as the cross-spectrum of the two input signals
x1,2(τ) (Smith 2007) C(t, f ) =
X1(t, f )X2∗(t, f )
, (3)
where the spectra X1,2(t, f ) are calculated in accordance with Eq. 2, and the asterisk means complex conjugate. Similarly to the full power mode, the product of two spectra is calculated in sev-eral consecutive overlapping time windows, which are averaged further providing a smoothed estimate of the coherence function
C(t, f ). As for the spectrogram, it is calculated in a set of
dis-crete values defined by the frequency channel separation ∆ f and time resolution ∆ta. We note that, in contrast to the case of the full power mode, the absolute value in Eq. 3 is evaluated after averaging the complex product X1(t, f )X2∗(t, f ) over Na consecu-tive windows. The conceptual difference of the correlation mode compared to the full power one is the efficient suppression of undesired signal components that occur in only one of the two inputs. The suppression naturally appears as a result of averag-ing with the time constant ∆ta used in smoothing the estimate of coherence. Some details pertaining to the usage of the cor-relation mode in the two-array, multi-beam setting of the radio telescope UTR-2 are described in the next section, and an exam-ple illustrating the suppression of the undesired signals in both the correlation and full power modes are given in Appendix B.
4. Use of the receiver with UTR-2 decameter array
The advantages of the receiver discussed here, especially the ef-ficiency of simultaneous usage of two input-output channels for reducing the signal confusion and improving RFI immunity, can be most clearly illustrated with operation at the decameter radio telescope UTR-2 (Kharkov, Ukraine (Braude et al. 1978)) that allows us to exploit the full range of receiver capacities due to its multi-beam architecture. The UTR-2 telescope is a phased array of 2040 dipole antennas grouped into two rectangular branches, north-south (NS) and east-west (EW), positioned in the form of a letter T and oriented along the local meridian and parallel, re-spectively, at coordinates 36◦56′E longitude and +49◦38′ lati-tude. The telescope has no mobile part, and pointing is achieved by means of phasing, computer-controlled delays, and the sum-mation of groups of antennas, independently for the EW and NS branches. Five summations are performed in parallel for the NS branch, so that it targets a 5-beam pattern on the sky (with a separate output per beam). Beams are separated by 30′
inter-vals along the north-south direction. The arrays thus produce five electronically steered main lobes of radiation pattern of area ∼ 14◦× 30′oriented along the east-west direction and ∼ 1◦× 14◦
EW-array beam NS-array beam Pencil-beam Pencil-beam area Source Confusion source E1 E1 E2 E0 E2
Fig. 1. Sketch of the geometry of UTR-2 beams on the sky, when the source of interest is located in the common part of the EW and NS lobes
in the north-south one. Secondary lobe levels are ≤ −12.5 dB below the main ones, and will not be taken into account here.
The availability of five simultaneous beams allows us to de-sign an efficient observational strategy for detecting weak radio sources such as, for example, the radio signals from exoplanets (Ryabov et al. 2004a; Ryabov et al. 2004b) or Saturn lightning (Griessmeier et al. 2008) in the presence of strong in-band inter-ference (Zarka et al. 1997). This strategy consists of the simul-taneous recording of signals coming from (at least) two out of five beams, one of which is directed towards the source of in-terest (ON beam) and the other in an arbitrary direction (OFF beam, generally ∼ 1◦ away from the target). Most signals of
terrestrial origin pollute both the ON and OFF beams, so one can develop a post-processing filtering algorithm that recignizes simultaneously occurring signals and removes them from the spectrograms. This procedure requires an (at least) two-channel receiver that is capable of simultaneously recording two parallel data streams corresponding to the two (ON and OFF) antenna configurations. To reach the maximum sensitivity, a typical ob-servation scheme uses a pre-detector sum of the signals from the two (EW and NS) arrays, thus enhancing the signal-to-noise ra-tio of the source located within the common part of the central lobes. It should be noted, however, that this method of creating an equivalent “pencil beam” radiation pattern of the whole ar-ray is affected by numerous confusion signals that often occur in one of the main lobes, outside of their common part (see, Fig. 1). This produces undesired patterns in the spectrograms and in-creases the difficulty of the low intensity (high-sensitivity) sig-nal asig-nalysis and interpretation. The pencil beam formation can be improved in full power mode by recording simultaneously the spectrograms of the sum and the difference of the EW and NS signals; the offline post-detector computation of the residual output (sum - difference), is equivalent to estimating the prod-uct EW×NS and thus strongly reduces the undesired patterns. In contrast, in correlation mode the coherence function is cal-culated directly and subsequently averaged as described in Sect. 3.3 hence reducing the confusion components as well.
We now consider the correlation between signals from the two antenna branches. Each beam can be assumed to be the sum of one pencil beam with two confusion lobes (i.e., the parts of the main lobe outside the pencil beam). We denote as E0(t) the elec-tric field of the wave received from the pencil beam, E1(t), the corresponding field from the confusion lobes of the EW branch,
and E2(t), the field from the confusion lobes of the NS branch. After combining the outputs from the two branches at the in-put of the ADC and performing baseband digitization (e.g., at 66 MHz sampling frequency), we derive two real-valued wave-forms:
EEW(t) = E0(t) + E1(t); ENS(t) = E0(t) + E2(t). (4) In estimating in real-time the spectral power of the waves ap-proaching the pencil beam, i.e., D|E0(t, f )|2
E
, where h...i means averaging over several (Na) consecutive data segments, we have two possibilities:
1. To compute the cross-correlation of the two waveforms (data streams), i.e., the average convolution between the two sig-nals c(t, τ) = EEW(t′) ∗ ENS(t′) = *Z T EEW(t′)ENS(t′+ τ)dt′ + . (5)
The averaging should be performed over a time interval that is much longer than the typical period(s) of the signal of in-terest (i.e., ∆ta>>1/ fmin). Substituting Eq. 4 into Eq. 5 and using the linearity of convolution and averaging operations, we have
c(t, τ) =E0(t′) ∗ E0(t′) + E0(t′) ∗ E2(t′) +
E1(t′) ∗ E0(t′) + E1(t′) ∗ E2(t′) .
The last three terms are small (uncorrelated signals) and hence can be discarded, while the first one corresponds to the autocorrelation of the pencil beam electric field. Using the Wiener-Khinchin theorem, the Fourier transform (FT) of
c(t, τ) infers the power spectrum in the pencil beam
D |E0(t, f )|2 E = √1 2π ∞ Z −∞ c(t, τ)ei2π f τdτ.
2. Alternately, we can first compute the spectra XEW,NS(t, f ) of each waveform in accordance with Eq.( 2). Owing to the lin-earity of FT, we obtain
XEW(t, f ) = X0(t, f ) + X1(t, f ); XNS(t, f ) = X0(t, f ) + X2(t, f ). Next, we can introduce the average of their cross product as XEW(t, f )XNS∗ (t, f ) =DX0(t, f )X0∗(t, f ) E + X0(t, f )X2∗(t, f ) + D X1(t, f )X0∗(t, f ) E + X1(t, f )X∗2(t, f ) ,
where the averaging is performed over Na >>1 elementary spectra. The last three terms should vanish in the limit Na→ ∞, and we again obtain
XEW(t, f )XNS∗ (t, f ) =D|X0(t, f )|2
E .
In principle, the two methods are strictly equivalent, the FT be-ing a linear transform. In practice, the second one is easier to implement in real-time in the receiver because of the availability of FFT algorithms. Another advantage of the second method is that the software AGC (automatic gain control) can be applied to the two spectra XEW,NS(t, f ) before multiplication and averag-ing, to ensure that the result is insensitive to gain fluctuations.
However, AGC values derived from the broadband signal would be strongly affected by impulsive intense narrowband interfer-ence, thus a more effective solution is to use a non-linear filter (i.e., clipping intense signals in the XEW,NS(t, f ) spectra before multiplication and averaging, to reduce the impact of interfer-ence.
Taking all the above considerations into account, the optimal way to obtain the “pencil beam spectra” in correlation mode (that has been accepted and implemented in the receiver) is as fol-lows: (i) performing both the windowing and FFT of each wave-form, followed by (ii) clipping of values above a given threshold, (iii) deriving the cross product of one NS spectrum by the com-plex conjugate of the corresponding EW one, and (iv) averaging over several products of complex spectra before calculating the squared amplitude of the average.
5. Applications
We discuss two examples of using the receiver to observe de-cameter radio sources that produce non-trivial patterns in the dynamic spectrograms.
5.1. Jovian S-bursts
For the first example, we consider S-bursts from Jupiter, fast sporadic frequency-drifting pulses, generated in the Jovian mag-netosphere by streams of keV electrons accelerated by electric fields between Jupiter and Io, its volcanically active moon. S-bursts are known to exhibit very complicated patterns in the time-frequency plane (Ryabov et al. 2007; Ryabov et al. 1997) requiring resolutions of a few kHz in the frequency domain and a few milliseconds in the time domain.
The S-burst emission occurs during so-called decameter ra-dio storms, several-hour long events, which are predictable on the basis of the analysis of the geometric configuration be-tween the Earth, Jupiter, and Io (Genova et al. 1989). Although the occurrence of S-bursts from Jupiter is predictable, the re-quired temporal and frequency resolutions cannot be specified in advance because of the unpredictable morphology and rapid changes in S-burst shapes and fine structures. Therefore, an op-timal solution for studying this type of emission is the waveform mode, when all the information within the receiver frequency-band is preserved, and the analysis of the time-frequency pat-terns is performed offline, after observation.
An example of using the waveform mode to observe Jupiter is shown in Fig. 2, where we depict a fragment of an S-burst storm recorded with the UTR-2 array on March 13, 2005. In Fig. 2a,b, a spectrogram of duration ∼1 s calculated from the same waveform but at different resolutions is shown. A char-acteristic feature of the patterns seen in the spectrogram is the frequency drift, i.e., a rapid change in the emission peak fre-quency with time. The value of the frefre-quency drift is of im-portance for testing various models of the emission generation mechanism, magnetic field of Jupiter, and plasma instabilities in the vicinity of Jupiter (Zarka et al. 1996; Hess et al. 2009). The data presented in Fig. 2a was calculated at time and frequency resolutions of 2 ms and 4 kHz, respectively. From the visual in-spection of this figure, one can conclude, for example, that the two patterns numbered 1 and 2 are characterized by substantially different values of the frequency drift. However, after increasing the time resolution to 0.25 ms for a 4 kHz bandwidth, it becomes clear that the pattern 2 (denoted as B in Fig. 2b,c) consists of several frequency drifting components of approximately similar
frequency drift rate to the pattern 1 in Fig. 2a. A zoomed version of the square area shown in Fig. 2b is presented in Fig. 2c, which illustrates the complexity of the intrinsic structure of the S-burst pattern.
5.2. Low-frequency pulsar observations
In the second example, we consider the radio emission from pulsars in the decameter waveband. Pulsars are rotating neu-tron stars that are known as bright radio sources. The emission consists of periodic pulses produced by a rotating object into a sharply beamed radiation pattern. Every time the beam hits the Earth observer, a pulse of emission can be detected, in a similar way to a lighthouse. The pulses of emission are broad-band, i.e., the frequencies at which various pulsars have been found range from the X- and γ-rays to the decameter wave band. It should be noted, however, that because of the absence until now of high-sensitivity, interference-immune receiver systems, pulsar emis-sion in the decameter waveband has remained practically unex-plored.
Although at their origin the pulses are emitted at all fre-quencies simultaneously, they experience subsequent distortion in the time-frequency plane defined by the dispersion of radio waves propagating in the interstellar medium. In terms of dy-namic spectrogram analysis, this means that initially vertical lines in the dynamic spectra corresponding to individual pulses are transformed at the reception point into frequency drifting stripes of emission with a frequency-dependent drift rate. A typ-ical spectrogram of the powerful pulsar PSR0809+74 is shown in Fig. 3a. Dark lines crossing the spectrogram from high to low frequencies are intense single pulses dispersed by the interstellar medium. It should also be noted that the high sensitivity spectro-gram shown in Fig. 3a allows us to distinguish between the ef-fects of interplanetary scintillations (Gapper et al. 1982) (broad vertical intensity modulation bands) and pulse-to-pulse varia-tions in power at the source (Ritchings 1976) (some of the dis-persed pulses look brighter than their neighbours).
The law of interstellar dispersion is well-known (Manchester & Taylor 1977) and described by the equation
∆t = 107 1 f12 − 1 f22 DM 2.41 [ms] , (6)
where ∆t is the time delay between the pulse arrival times at the two frequencies, f1and f2, and f2 > f1, expressed in MHz. The parameter DM is then dispersion measure,which is given by an integral characteristic of the interstellar medium
DM =
Z
nedl = hnei D h
pc cm−3i,
where neis the electron density along the propagation path l and
D is the distance to the radio emission source. The parameter DM thus defines the pulse frequency drift rate at a given
fre-quency f to be d f dt = k f 3 MHz sec , (7)
where k = DM1.210−7 .The shape of the time-frequency patterns
of pulsar signals is defined by Eq. 6 and, therefore, the time and frequency resolutions necessary for observing pulsars can be easily derived. The requirement in terms of the frequency resolution can be obtained by considering a periodic sequence of frequency-drifting pulses passing through a single frequency channel of the spectrum analyzer (see Fig. 4).
f W p T f ' t
Fig. 4. Schematic of a periodic sequence of frequency-drifting pulses crossing a frequency channel of the spectrum analyzer
The time τ is an interval between successive pulses in the output of an elementary frequency channel of the spectrogram. The two pulses can be resolved if τ > 0, i.e., the pulses do not overlap. The condition of non-overlap can be formulated in terms of the frequency bandwidth ∆ f of a frequency channel, the frequency drift rate defined by Eq. 7, the dispersion mea-sure DM, the pulsar period Tp, and the duty cycle of the pulsar,
d, which is the fraction of time when the emission intensity is
above the noise level. The duty cycle of pulsars varies and is fre-quency dependent, but is typically in the range d ∼ 0.05 − 0.15 (Kuzmin et al. 1998).
From the sketch in Fig. 4, one can infer that τ =Tp(1 − d) − δt ,
where δt = k f∆ f3 as can be found from Eq. 7. We then have the
following condition for non-overlapping pulses, i.e., τ > 0:
Tp> ∆ f
k f3(1 − d) = 8.3 × 10 6 ∆ f
f3(1 − d). (8)
Here, Tpis in ms, DM in pc cm-3, and ∆ f and f are in MHz. It should also be noted that due to scattering processes in the interstellar medium, the pulse experiences additional frequency dependent broadening (Bhat et al. 2004), i.e., an additional term τbshould also be subtracted from the value of τ. In the case of a power-law spectrum of wave numbers in the scattering medium, τb follows the power law τb ∝ f1α, where α takes the value of 4.4 for a Kolmogorov-type spectrum. In the subsequent analysis, we, however, neglect this additional pulse broadening by assum-ing that its magnitude is much smaller than that defined by the dispersion measure, i.e., τb<< δt.
For the parameter values used in our observations with the UTR-2 array, i.e., a sampling frequency fs = 66 MHz, and a time window size of Nw= 16384 defining the frequency channel separation at ∆ f = 4 kHz), one can estimate which pulsars can be detected, e.g., by visual inspection of the dynamic spectra in the full power mode. In Fig. 5, we plot a scatter diagram of the values of DM versus Tpfor 56 pulsars (Kuzmin et al. 1998) and also for the Crab pulsar. Four solid lines, obtained with Eq. 8 at frequencies f = 6, 10, 10, 10 MHz for a value of duty cycle
d → 0 are also shown, together with dashed lines calculated at
the value of d = 0.15 (corresponding to a ∼ 54◦ pulse profile
width). The small distance between the solid and dashed lines indicates that the main part of the pulse distortion is defined by the dispersion time δt, so that a non-zero value of the duty cycle
d can be neglected for an approximate analysis of almost all the
pulsars considered here.
All the points shown in Fig. 5, except the one of the Crab pulsar, are located below the line f = 30 MHz and, therefore, these pulsars are resolved by the 4 kHz frequency channels. The pulses from the Crab pulsar cannot be detected in the decame-ter waveband with a 16384-point FFT at sampling frequency 66
Fig. 5. Dispersion measure vs. period for 56 pulsars (Kuzmin et al. 1998) (diamonds) and for the Crab pulsar (crossed diamond). Four lines calculated with Eq. 8, corresponding to the frequencies of 6, 10, 20, and 30 MHz, delimit the lower limits of the areas where the pulsars can be detected with a receiver of 4 kHz frequency resolution. Solid and dashed lines correspond to different values of the parameter d defining the pulsar duty cycle: d = 0 and d = 0.15, respectively. For example, the pulsar PSR0809+74 (crossed diamond) is observable at any frequency above ∼6 MHz, whereas the Crab pulsar cannot be detected at this frequency resolution in the whole frequency band of UTR-2 array (8-32 MHz)
MHz. On the other hand, it is possible to resolve these pulses in the waveform mode if it is set to the frequency resolution at 0.25 kHz by using a 262144-point FFT in the post-processing. In such case, the point corresponding to the Crab pulsar shifts to the region of detectability between the lines of 10 MHz and 20 MHz in Fig. 5, therefore the pulse sequences should become visible in the frequency range 10 MHz < f < 20 MHz.
We note that the alternative method of coherent dedisper-sion (Lorimer & Kramer 2005) can be applied to waveform data to compensate for the effect of the interstellar medium. This method is renowned for achieving greater timing accuracy in studying the pulse profiles and, moreover, it can easily be imple-mented into software. Once the data is recorded in the waveform mode, the advantage of building an optimal coherent dedisper-sion algorithm can be taken in subsequent processing.
Many pulsars that appear between the lines at f =10 MHz and f =30 MHz in Fig. 5 can thus be successfully observed within the observational band of the UTR-2 array (8-32 MHz). It should be noted, however, that because of decay of the radio waves in the ionosphere at low frequencies, the detection of in-dividual pulses below ∼12 MHz is a rare event in observations with UTR-2, which occurs only for the most powerful pulsars, e.g., PSR0809+74 shown in Fig. 3. Despite the low SNR and slow frequency drift rate, two pulses can be clearly identified by eye in Fig. 3b.
We finally sort in Table 2 the pulsars according to their ob-servability with the full power mode at 4 kHz frequency resolu-tion. The pulsars in the first column can be observed in a wide frequency band, sometimes even below 10 MHz. The second and third columns contain pulsars that are resolved in the upper fre-quency part of the spectrogram only. The pulsars in the last col-umn may be problematic to observe at 4 kHz resolution. The individual pulses from those pulsars are expected to be resolved only when observed in the waveform mode.
Table 2. Pulsar list from (Kuzmin et al. 1998)
f < 10MHz 10MHz < f < 20MHz f > 20MHz PSR PSR PSR 0011+47 0138+59 1706-16 0136+57 0154+61 0329+54 1749-28 0355+54 0301+19 0450-18 1953+50 0540+23 0525+21 0450+55 2016+28 0740-28 0809+74 0628-28 2020+28 1737-30 0834+06 0655+64 2021+51 1742-30 0950+08 0656+14 2111+46 1804-08 1133+16 0818-13 2154+40 1826-17 1237+25 0820+02 2217+47 1845-01 1530+27 0823+26 2224+65 1933+16 1822-09 0919+06 2306+55 CRAB 1839+56 1508+55 2310+42 1929+10 1541+09 2319+60 1952+29 1604-00 2351+61 2045-16 1642-03 2110+27 1702-19 6. Conclusion
Using up-to-date digital components that have become com-mercially available, interference-immune design, and optimized real-time signal processing algorithms, we have developed a dig-ital receiver that has strong potential to obtain high-resolution spectral images in LF radio astronomy.
To our knowledge, receivers combining characteristics such as multiple working regimes, high sensitivity, low level of spu-rious signals, and software interfaces adapted for LF radio ob-servations have not been reported to date. As illustrated by two examples of observations performed with the receiver in the de-cameter wave band, the receiver has a high flexibility of op-eration modes, i.e., the working parameters can be tuned to optimize the reception of both sporadic and stationary types of radio signals. Besides the exploration of the radio emis-sion from well-known objects such as Jupiter, Sun, and pul-sars, the receiver can also be used for detecting and analyz-ing other radio sources, previously unexplored with ground-based instruments. Those include, for example, Saturn’s light-ning (Griessmeier et al. 2008), flaring stars (Abranin et al. 1997; Konovalenko et al. 2008), the elusive radio emission from exo-planets (Weber et al. 2007; Ryabov et al. 2004b).
Non-trivial fine spectral structures, unresolved by previously existing receiver equipment, are detected in the high-resolution spectrograms of Jupiter S-burst emissions. We found that many of the complex S-burst spectral patterns in the time-frequency plane consist of elementary coherent sub-bursts of duration 5-10 ms. A typical example of this division of large spectral patterns into smaller ones is presented in Fig. 2c. This property of S-burst patterns is a new finding, and will be studied further in a separate paper.
Another important but poorly studied class of decameter ra-dio sources, rara-dio pulsars, has also been discussed in the paper. The requirement of a receiver system capable of resolving pow-erful sequences of individual pulses (possibly including giant pulses (Cordes et al. 2004)) in the spectrograms is formulated in terms of the pulsar period and duty cycle, taking also into ac-count wave propagation effects. An example showing the feasi-bility of observing separate pulses from the pulsar PSR0809+74 is given, down to the low-frequency limit determined by the Earth’s ionospheric cutoff. An estimate of the parameters nec-essary to detect sequences of pulses is also formulated for the
Crab pulsar as well as many other pulsars previously studied at higher frequencies.
Acknowledgements. The receiver had been created, installed and
commis-sioned within the framework of joint France-Japan-Ukraine-Austria project CNRS/ANR project n◦NT05-1 42530 ”The direct detection (and study) of exo-planets using radio waves”.
References
Abranin, E. P., Bazelyan, L. L., Alekseev, I. Y., et al. 1997, Ap&SS, 257, 131 Bendat, J. S., & Piersol, A. G. 1986, Random data. Analysis and Measurement Procedures (New York: Wiley)
Bhat , N. D. R., Cordes, J. M.,Camilo, F., et al. 2004, ApJ, 605, 759 Boischot, A.,Rosolen, C., Aubier, M. G., et al. 1980, Icarus, 43, 399 Braude, S. Y., Megn, A. V.,Ryabov, B. P., et al. 1978, Ap&SS, 54, 3 Briand, C., Zasvlasky, A., Maksimovic, M., et al. 2008, A&A, 490, 3398 Cordes, J. M., Bhat, N. D. R., Hankins, T. H., et al. 2004, ApJ, 612, 375 Fitzgerald, W. J., Smith, R. L., Walden, A. T., & Young, P. C. 2000, Nonlinear and nonstationary signal processing (Cambridge: Cambridge Univ. Press) Gapper, G. R., Hewish, A., Purvis, A., & Duffet-Smith, P.J. 1982, Nature, 296, 633
Genova, F., Zarka, P., & Lecacheux, A. in Time-variable Phenomena in the Jovian System, ed. M. J. S. Belton, R. A. West, and J. Rahe (NASA SP-494) 156
Griessmeier, J.-M., Zarka, P., Konovalenko, A., et al. 2008, Geophysical Research Abstracts, 10, EGU2008-A-09350
Hess, S., Zarka, P., Mottez, F., & Ryabov, V. B. 2009, P&SS, 57, 23
Johnson, J. T., Niamsuwan, N., & Ellingson, S. W. 2005, in Proceedings of the 2005 Earth-Sun System Technology Conference (ESTC2005), June 28-30, 2005, Maryland, USA
Kleewein, P. C., Rosolen, C., & Lecacheux, A. 1997, in Planetary Radio Emissions IV, ed. H. O. Rucker, S. J. Bauer, & A. Lecacheux (Vienna: Austrian Acad. Sci. Press) p. 349
Konovalenko, A. A., Rucker, H. O., Lecacheux, A., et al. 2008, Geophysical Research Abstracts, 10, EGU2008-A-08201
Kuzmin, A. D., Izvekova, V. A., Shitov, Yu. P., et al. 1998, A&AS, 127, 355 Lecacheux, A., Konovalenko, . ., & Rucker, .. 2004, P&SS, 52, 1357 Lorimer, D.R., & Kramer, M. 2005, Handbook of Pulsar Astronomy, (Cambridge: Cambridge University Press)
Manchester, R. N., & Taylor, J. H. 1977, Pulsars (San Francisco: Freeman) Melnik, V. N., Rucker, H. O., Konovalenko, A. A., et al. 2008, in Solar Physics Research Trends, ed. P. Wang, (New York, Nova Sci. Publ.) p. 287
Ritchings, R. T. 1976, MNRAS, 176, 249
Rosolen, C., Clerc, V., & Lecacheux, . 1999, Radio Sci. Bull. 291, 6 Ryabov, B. P., Zarka, P., Rucker, H. O., et al.1997, in Planetary Radio Emissions IV, ed. H. O. Rucker, S. J. Bauer, & A. Lecacheux (Vienna: Austrian Acad. Sci. Press), p. 65
Ryabov, V. B., Zarka, P., & Ryabov, B. P. 2004, in Proc. Of Joint AOGS 1st Annual Meeting & 2nd APHW Conference, 5-9 July 2004, Singapore, p.385 Ryabov, V. B.,Zarka, P., & Ryabov, B. P., P&SS, 52, 1479
Ryabov, V. B., Ryabov, B. P., Vavriv, D. M., et al. 2007, JGR, 112, A09206 Smith, J. O. 2007, Mathematics of the Discrete Fourier Transform (DFT): with Audio Applications (W3K Publishing)
Tukey, J. W. 1967, in. Spectral analysis of time series, ed. B. Harris (John Wiley and sons)
Weber, R., & Faye, C. 1998, in: Signal Analysis and Prediction, ed. Prochazka et al., (Boston: Birkhauser)
Weber, R., Viou, ., Coffre, ., et al. 2005, EURASIP Journal n Applied Signal Processing, 16, 2686
Weber, R., Zarka, P., Ryabov, V. B., et al. 2007, Proc. of EUSIPCO 2007 Conference, 3-7 September 2007, Pozna, Poland
Zarka, P., Farges, T., Ryabov, B. P., et al. 1996, GRL, 23, 125
Zarka, P., Queinnec, J., Ryabov, B.P., et al. 1997, in Planetary Radio Emissions IV, ed. H. O. Rucker, S. J. Bauer, & A. Lecacheux (Vienna: Austrian Acad. Sci. Press)
Zarka, P., Treumann, R. A., Ryabov, B. P., & Ryabov, V. B. 2001, Ap&SS, 277, 293
Appendix A: Receiver performance and technical solutions
The receiver concept is based on direct baseband data recording without any frequency conversion. This approach allows us to
avoid difficulties caused by strong in-band interference signals. The hardware of the digital receiver consists of two parts (see Fig. A.1c,d): an ADC module and a DSP board. A block dia-gram of the receiver is shown in Fig. A.2. The ADC and DSP boards are connected either via a two-channel 5Gbit/sec serial data link (if both boards are installed in a single host PC) or op-tical fibers providing data transfer over a long distance (up to 10 km). In the ADC module, LTC2208 16-bit A/D converters are used. Data buffers and channel logics are realized with the FPGA Spartan3. The input data streams can be sampled at any rate defined by either internal or external clock, up to 130 MHz. The DSP board design is based on the Xilinx Virtex-II 3000 chip used as a FPGA (field-programmable gate array), and, in addition, has a fixed-point signal processor TMS320C6416 and a 256 Mbyte on-board SDRAM memory module. The DSP board is designed as a X extension card, which supports the PCI-X64/66 standard interface for the communication with the host PC. Different modes of signal processing can be achieved by the receiver using the FPGA and the signal processor capabilities.
To reduce the impact of spurious signals generated in the DSP board and other circuits of the host PC, the ADC module is manufactured as a separate block . This engineering solution, as well as the elaborate shielding of sensitive elements, allowed us to achieve both a high SFDR value and a low level of noise floor (see Table 1). In particular, the SFDR parameter is crucial for radio astronomical observations, where weak signals from natural radio sources should be detected with the background of powerful in-band interference of terrestrial origin (mostly man-made). Therefore, serious efforts were undertaken to increase the SFDR-value. Among them, we mention an automatic digital DC bias compensation, and data dithering performed while trans-ferring data to the DSP board via the serial link. The theoreti-cal maximum SNR (or dynamic range) for the 16-bit LTC2208 A/D converter used is 78 dBFS, whereas an effective value of 74 dBFS was practically achieved.
The digitized data flow from the ADC is supplied to the DSP board, where a real-time, windowed FFT with or without a 50%-overlap, as well as spectral averaging, are performed in the FPGA. A modified 16384-point FFT algorithm was imple-mented in the receiver that provides access to 8192 frequency channels. To improve the performance of the FFT calculation, a method of computing a single complex FFT for two real-valued signals (from the two input channels) with subsequent data re-ordering was applied. The windowing is realized via multipli-cation by values of window-function coefficients of 18 bits pre-cision, which is downloaded to the DSP memory as a table of values at the stage of initializing the receiver before the start of data recording.
The fixed-point, digital signal processor TMS320C6416 pro-vides an additional computing power, and is used to control the data transfer from the FPGA to the PCI-X controller and per-form extra calculations, if necessary. For example, it is possible, when the signal processor is used in combination with the on-board RAM memory buffer, to implement real-time algorithms of RFI mitigation in the frequency domain, and/or compensate for a non-uniformity of the frequency response function of the antenna system.
In the waveform mode, the receiver is capable of continuous data transfer at a maximum rate of 260 Mbyte/sec via the PCI-X64/66 interface for writing the data to the array of hard disks organized as a RAID-0 system in the host computer.
For controlling the receiver parameters, the data acquisition process, and the real-time display, original software was devel-oped. The software operates under the Windows’NT/2K/XP
op-a)
b)
c)
d)
e)
hTG GG GFig. A1. Signal path from the antenna system to the
control display of the host computer. a) UTR-2
antenna array; b) anti-alias filters and amplifiers
block; c) ADC module; d)
in to a PCI-X slot of the host PC; e) snapshot of the
host PC display during an observation session.
Fig. A.1. Signal path from the antenna system to the control displayof the host computer. a) UTR-2 antenna array; b) anti-alias filters and amplifiers block; c) ADC module; d) DSP board to be plugged into a PCI-X slot of the host PC; e) snapshot of the host PC display during an observation session
erating system and is organized as a network server. The in-troduction of LAN support and control of the receiver ensures various possible modes of remote diagnostics and parameter ad-justment. For example, a regime of remote operation is essential in long-duration unattended observations, when the interaction of the observer with the data acquisition process is not required within, say, a night of observations. An example of the receiver control panel and real-time data visualization display is given in Fig. A.3.
Other characteristics of the receiver should also be men-tioned. The receiver has a perfect linearity over its full dynamic range, and a calibration mode. A specific software allows us to use the receiver in an unattended mode, i.e., for automated obser-vations of several radio sources. It can also be used as a compo-nent of more complicated astronomical data acquisition systems in combination with filtering system designed for observing spe-cific radio sources and augmented with real-time RFI mitigation techniques. Further options include a choice of windowing func-tion in FFT, pre-selecfunc-tion of the frequency band to be recorded to the hard disk (programmable bands), automated script control of the observation sessions, digital down-conversion of the ob-servation frequency band, and implementation of automatic gain control for compensating the frequency response of the antenna, cables, preamplifiers, and input filter system.
Appendix B: Using a receiver in correlation mode with the UTR-2 array
We consider computer-simulated input signals assumed to orig-inate in the NS and EW arrays defined as follows:
– EW-array: two harmonic components of dimensionless
am-plitudes A1 = 0.05, A2 = 0.075, and frequencies f1 = 21.0, f2 = 24.2 coming from the common part of the beams (pen-cil beam) plus a confusion harmonic component of ampli-tude A3 = 0.1 and frequency f3 = 25.2. Two independent realizations ξ1,2(t) of white Gaussian noise and unit variance were added to both parts simulating the sky background fluc-tuations in the pencil beam and the remaining part of the EW-lobe.
– NS-array: theame two harmonic components and noise
orig-inating in the pencil beam and another independent Gaussian noise component ξ3(t) representing the sky background fluc-tuations.
With the same notations as Sect. 4, we then have:
EEW(t) = E0(t) + E1(t),
E0(t) = A1cos(ω1t + ψ1) + A2cos(ω2t + ψ2) + ξ1(t), E1(t) = A3cos(ω3t + ψ3) + ξ2(t),
ENS(t) = E0(t) + E2(t), E2(t) = ξ3(t),
where ψ1,2,3 are the independent random values for the initial phases of the harmonic components, ω1,2,3= 2π f1,2,3. The spec-tral analysis was performed by both methods described in Sects. 3.2 and 3.3, and the results are presented in Fig. B.1. Figures ( B.1, a and b) depict the power spectra of ENS and EEW, respec-tively, calculated at a single step of the full power mode (aver-aged over Na consecutive non-overlapping data segments). One can easily recognize two peaks at f1 = 21.0, and f2 = 24.2 cor-responding to the source in the pencil beam, whereas the peak at f3 = 25.2, representing a confusion signal in the EW-array, is seen only in Fig. B.1b. The result of the pre-detector addition of
the two waveforms from the two beams (i.e., before making FFT, squaring and smoothing) with subsequent processing in the full power mode is shown in Fig. B.1c, where the peaks at f = f1,2 become stronger, since the signal is present in both the EW and NS beams, while the power of the confusion signal at f = f3 is somewhat reduced because of the absence of this component in the NS beam. The complete suppression of the confusion sig-nal due to averaging is demonstrated further in Fig. B.1d, where we show the result of the calculation in the correlation mode with the same value of integration time Na = 128. One can con-clude that the confusion signal is completely suppressed, while the signal-to-noise ratio remains approximately the same as that in the full power mode.
Appendix C: Acronyms
ADC Analog to Digital Converter dBc deciBels relative to the carrier dBFS deciBels relative to Full Scale DM Dispersion Measure
DSP Digital Signal Processor ENOB Effective Number Of Bits (F)FT (Fast) Fourier Transform FPGA Field-Programmable Gate Array ITU International Telecommunication Union HF High Frequencies (< 30 MHz)
LEO Low Earth Orbit
LF Low Frequencies
LOFAR LOw Frequency ARray LWA Long Wavelength Array RFI Radio Frequency Interference SFDR Spurious Free Dynamic Range SNR Signal to Noise Ratio
UTR-2 Ukrainian T-shape Radiotelescope Mark 2 VHF Very High Frequencies (> 30 MHz)
1
2
A
B
A
B
a)
b)
c)
Fig. 2. Spectrograms of Jupiter S-bursts calculated from a waveform recorded on March 13, 2005. a) Time and frequency resolutions are 2 ms and 4 kHz, respectively. The fine structure of the S-burst patterns is blurred; b) time and frequency resolutions are 0.25 ms and 4 kHz, respectively; c) zoomed image of the area enclosed by white rectangle in plate b).
a)
b)
Fig. 3. Spectrograms of the pulsar PSR0809+74 recorded in full power mode. The grey-color scale represents the spectral power (white color corresponds to zero-intensity, the dark areas indicate powerful signals). a) Wide-band sequence of frequency-drifting pulses recorded on December 13, 2006; b) Low-frequency pulses recorded on December 14, 2006 close to the ionospheric cut-off frequency, but still far above the limit imposed by the channel bandwidth (Eq. 8)
Instantaneous spectrum (1st channel) Data files Menu -trees Color and contrast panel Shortcut control buttons Instantaneous spectrum (2ndchannel) Real-time dynamic spectrum:
frequency -horizontal axis, time - vertical axis
(1st channel)
Real-time dynamic spectrum: frequency -horizontal axis,
time - vertical axis (2nd channel)
Fig. B.1. Computer simulation of the effect of suppressing the confusion signal by using cross-correlated spectra. a) Power spectrum of the signal in the NS-array containing two harmonic components and background noise; b) Same as a), but for the EW array, where the third harmonic component corresponds to the confusion signal; c) Spectrum of the sum of the signals from the two arrays in the simple full power mode; d) Coherence function, i.e., the averaged complex product of the two complex spectra, where the confusion component is fully suppressed.
